JEE PYQ: Indefinite Integration Question 22
Question 22 - 2019 (09 Apr Shift 2)
If $\int e^{\sec x}(\sec x\tan x,f(x) + (\sec x\tan x + \sec^2 x)),dx = e^{\sec x}f(x) + C$, then a possible choice of $f(x)$ is:
(1) $\sec x + \tan x + \frac{1}{2}$
(2) $\sec x - \tan x - \frac{1}{2}$
(3) $\sec x + x\tan x - \frac{1}{2}$
(4) $x\sec x + \tan x + \frac{1}{2}$
Show Answer
Answer: (1)
Solution
Using $\int e^{g(x)}(g’(x)f(x) + f’(x)),dx = e^{g(x)}f(x) + C$ with $g(x) = \sec x$, $g’(x) = \sec x\tan x$. So $f’(x) = \sec x\tan x + \sec^2 x$. Integrating: $f(x) = \sec x + \tan x + C_0$. Option (1) with $C_0 = \frac{1}{2}$ works.
BETA
